Optimal design of conductive natural branched pathways for cooling a heat‐generating volume

Abstract

The application of constructal networks to cool a heat‐generating volume has been the subject of many research studies in the past decade. However, the current volume‐point constructs mainly include rectangular, triangular, and parabolic‐shaped constructs, and none of them are similar to the constructs of common plant leaves in nature. A bionic quadrilateral volume based on the shape of common leaf veins is proposed, and the heat‐conductive model of the quadrilateral volume is established. The analysis results show that the minimal peak temperature difference can be as low as 1.3k when the porosity α1 of the quadrilateral volume is equal to 0.15; the recommended value of interval number n of central link is 30, the optimal value of exponent m1 of the width of central link is about 0.9; and the optimal value of the aspect ratio H1/L1 remains nearly constant at 0.7. When the quadrilateral volume obtains highest heat conductivity, the branching cooling links should be perpendicular to the central link.

Multi-Objective Constructal Design for Square Heat-Generation Body with “Arrow-Shaped” High-Thermal-Conductivity Channel

“…Ribeiro and Queiros-Condé [36] obtained optimal constructal design of the "I-shaped" HTCC in a square HGB. Zhu et al [37] obtained optimal constructal design of the vein-like HTCC in a quadrilateral HGB, and that was different from the optimal constructal design obtained by minimizing the MTD [32].…”

“…Hajmohammadi et al [31] devised a model in which HTCCs are embedded in annular fins to assist heat dissipation, and achieved constructal design of HTCCs with minimum MTD. Li and Feng [32] proposed a quadrilateral HGB model with embedded vein-like HTCCs, and obtained optimal constructal design of this model by with the objective of minimizing the MTD.…”

Multi-Objective Constructal Design for Quadrilateral Heat Generation Body with Vein-Shaped High Thermal Conductivity Channel

“…Hajmohammadi et al [ 49 ] established an annular fin model embedded with HTCCs and obtained the optimal constructal of the HTCCs by minimizing the MTD. According to the common plant leaf veins in nature, Li and Feng [ 50 ] proposed a quadrilateral HGB model embedded with vein-shaped HTCCs and obtained its optimal constructal by minimizing the MTD.…”

“…Zhu et al [ 56 ] further gained the optimal constructal of the quadrilateral HGB established in Ref. [ 50 ] with the minimum EGR. The research showed that the optimal constructal with the minimum EGR is different from that obtained by minimizing the MTD.…”

Constructal optimization of heat conduction with minimum entransy dissipation rate for leaf-shaped quadrilateral heat-generating body

“…究了圆盘形产热体的最优构形，分析了不同设计参数对产热体最优构形的影响；Lorenzini 等 [43,44] 考虑高导热材料和产热区域之间存在接触热阻， 分别对内嵌有 I 形 [43] 和 T 形 [44] 高导热 通道的方形产热体进行了构形优化，结果表明考虑接触热阻对最大温差最小值有较大影响； Bejan 等 [45] 同时考虑了传导和强度性能要求，研究了复合结构的最优构形。随着构形理论的 发展，一些学者认为具有天然分支结构的树叶可以为电子元件产热体的散热结构提供指导。 Li 和 Feng [46] 在前人研究的矩形、三角形、圆盘形和方形产热体的基础上，进一步基于常见 叶脉形状的仿生四边形建立了叶形四边形产热体模型，并以最大温差最小为优化目标，对其 进行了构形研究。 最大温差仅体现产热体承受温度的极限，并不能体现产热体的平均散热性能，因此一些 学者进一步基于火积耗散率最小研究了各种产热体的最优构形。肖庆华等 [47] 研究了矩形单元 构造体的最优构形，发现构造体的平均传热温差随着构造体级数的增加而逐渐减小；魏曙環 等 [48] 研究了三角形单元构造体的最优构形，并与最大温差最小下的最优构形进行了比较， 结果表明火积耗散率最小下的平均传热温差更低；陈林根等 [49] 对文献 [42]中的辐射状圆盘产热 体重新进行了构形优化，得到了平均传热温差更小的圆盘产热体构形；Liu 等 [50] 分别建立了 宏观尺度和微尺度下的辐射状圆盘导热模型，将点状冷源分布在圆周侧，以传热过程中的火 积耗散率最小为目标对均匀产热的圆盘开展了构形优化，结果表明微尺度下的构形高导热通 道更有利于降低导热热阻；冯辉君等 [51] 研究了内嵌有"+"形高导热通道的方形产热体的最优 构形，同时考虑产热体内的热应力性能，开展了实验研究，验证了以火积耗散率最小为目标能 使产热体传热性能提高，同时温度梯度更加均匀。除了产热体外，火积理论还被应用在其它构 形优化中。冯辉君等 [52,53] 基于火积耗散率对有机工质管壳式换热器 [52] 和冷凝器 [53] 进行了构形 优化；陈林根等 [54] 基于火积耗散率对船用锅炉进行了构形优化。 本文在文献 [46]…”